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49 relations: Boundary element method, Computational fluid dynamics, Continuum mechanics, Deformation (mechanics), Differential equation, Diffuse element method, Discrete least squares meshless method, Dissipative particle dynamics, Euler equations (fluid dynamics), Extended finite element method, Finite difference method, Finite element method, Finite point method, Finite pointset method, Finite volume method, Flow velocity, Frozen (2013 film), Galerkin method, Gaussian quadrature, Generalized-strain mesh-free formulation, Immersed boundary method, International Journal of Computational Methods, Kronecker delta, Lagrange multiplier, Lagrangian and Eulerian specification of the flow field, Material point method, Mesh generation, Method of fundamental solutions, Moving least squares, Moving particle semi-implicit method, Navier–Stokes equations, Numerical analysis, Numerical differentiation, Numerical integration, Numerical methods for ordinary differential equations, Particle-in-cell, Partition of unity, Patch test (finite elements), Petrov–Galerkin method, Plasticity (physics), Reproducing kernel particle method, Smoothed finite element method, Smoothed-particle hydrodynamics, Stencil code, Ted Belytschko, Types of mesh, Viscous vortex domains method, Weak formulation, Weakened weak form.
Boundary element method
The boundary element method (BEM) is a numerical computational method of solving linear partial differential equations which have been formulated as integral equations (i.e. in boundary integral form).
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Computational fluid dynamics
Computational fluid dynamics (CFD) is a branch of fluid mechanics that uses numerical analysis and data structures to solve and analyze problems that involve fluid flows.
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Continuum mechanics
Continuum mechanics is a branch of mechanics that deals with the analysis of the kinematics and the mechanical behavior of materials modeled as a continuous mass rather than as discrete particles.
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Deformation (mechanics)
Deformation in continuum mechanics is the transformation of a body from a reference configuration to a current configuration.
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Differential equation
A differential equation is a mathematical equation that relates some function with its derivatives.
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Diffuse element method
In numerical analysis the diffuse element method (DEM) or simply diffuse approximation is a meshfree method.
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Discrete least squares meshless method
The discrete least squares meshless (DLSM) method is a newly introduced meshless method based on the least squares concept.
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Dissipative particle dynamics
Dissipative particle dynamics (DPD) is a stochastic simulation technique for simulating the dynamic and rheological properties of simple and complex fluids.
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Euler equations (fluid dynamics)
In fluid dynamics, the Euler equations are a set of quasilinear hyperbolic equations governing adiabatic and inviscid flow.
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Extended finite element method
The extended finite element method (XFEM), is a numerical technique based on the generalized finite element method (GFEM) and the partition of unity method (PUM).
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Finite difference method
In mathematics, finite-difference methods (FDM) are numerical methods for solving differential equations by approximating them with difference equations, in which finite differences approximate the derivatives.
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Finite element method
The finite element method (FEM), is a numerical method for solving problems of engineering and mathematical physics.
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Finite point method
The finite point method (FPM) is a meshfree method for solving partial differential equations (PDEs) on scattered distributions of points.
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Finite pointset method
In applied mathematics, the name finite pointset method is a general approach for the numerical solution of problems in continuum mechanics, such as the simulation of fluid flows.
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Finite volume method
The finite volume method (FVM) is a method for representing and evaluating partial differential equations in the form of algebraic equations.
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Flow velocity
In continuum mechanics the macroscopic velocity, also flow velocity in fluid dynamics or drift velocity in electromagnetism, is a vector field used to mathematically describe the motion of a continuum.
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Frozen (2013 film)
Frozen is a 2013 American 3D computer-animated musical fantasy film produced by Walt Disney Animation Studios and released by Walt Disney Pictures.
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Galerkin method
In mathematics, in the area of numerical analysis, Galerkin methods are a class of methods for converting a continuous operator problem (such as a differential equation) to a discrete problem.
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Gaussian quadrature
In numerical analysis, a quadrature rule is an approximation of the definite integral of a function, usually stated as a weighted sum of function values at specified points within the domain of integration.
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Generalized-strain mesh-free formulation
The generalized-strain mesh-free (GSMF) formulation is a local meshfree method in the field of numerical analysis, completely integration free, working as a weighted-residual weak-form collocation.
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Immersed boundary method
In computational fluid dynamics, the immersed boundary method originally referred to an approach developed by Charles Peskin in 1972 to simulate fluid-structure (fiber) interactions.
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International Journal of Computational Methods
The International Journal of Computational Methods has been published by World Scientific since 2004.
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Kronecker delta
In mathematics, the Kronecker delta (named after Leopold Kronecker) is a function of two variables, usually just non-negative integers.
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Lagrange multiplier
In mathematical optimization, the method of Lagrange multipliers (named after Joseph-Louis Lagrange) is a strategy for finding the local maxima and minima of a function subject to equality constraints (i.e., subject to the condition that one or more equations have to be satisfied exactly by the chosen values of the variables).
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Lagrangian and Eulerian specification of the flow field
In classical field theory the Lagrangian specification of the field is a way of looking at fluid motion where the observer follows an individual fluid parcel as it moves through space and time.
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Material point method
The material point method (MPM) is a numerical technique used to simulate the behavior of solids, liquids, gases, and any other continuum material.
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Mesh generation
Mesh generation is the practice of generating a polygonal or polyhedral mesh that approximates a geometric domain.
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Method of fundamental solutions
In scientific computation and simulation, the method of fundamental solutions (MFS) is getting a growing attention.
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Moving least squares
Moving least squares is a method of reconstructing continuous functions from a set of unorganized point samples via the calculation of a weighted least squares measure biased towards the region around the point at which the reconstructed value is requested.
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Moving particle semi-implicit method
The moving particle semi-implicit (MPS) method is a computational method for the simulation of incompressible free surface flows.
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Navier–Stokes equations
In physics, the Navier–Stokes equations, named after Claude-Louis Navier and George Gabriel Stokes, describe the motion of viscous fluid substances.
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Numerical analysis
Numerical analysis is the study of algorithms that use numerical approximation (as opposed to general symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics).
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Numerical differentiation
In numerical analysis, numerical differentiation describes algorithms for estimating the derivative of a mathematical function or function subroutine using values of the function and perhaps other knowledge about the function.
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Numerical integration
In numerical analysis, numerical integration constitutes a broad family of algorithms for calculating the numerical value of a definite integral, and by extension, the term is also sometimes used to describe the numerical solution of differential equations.
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Numerical methods for ordinary differential equations
Numerical methods for ordinary differential equations are methods used to find numerical approximations to the solutions of ordinary differential equations (ODEs).
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Particle-in-cell
The particle-in-cell (PIC) method refers to a technique used to solve a certain class of partial differential equations.
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Partition of unity
In mathematics, a partition of unity of a topological space X is a set R of continuous functions from X to the unit interval such that for every point, x\in X,.
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Patch test (finite elements)
The patch test in the finite element method is a simple indicator of the quality of a finite element, developed by Bruce Irons.
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Petrov–Galerkin method
The Petrov–Galerkin method is a mathematical method used to obtain approximate solutions of partial differential equations which contain terms with odd order.
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Plasticity (physics)
In physics and materials science, plasticity describes the deformation of a (solid) material undergoing non-reversible changes of shape in response to applied forces.
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Reproducing kernel particle method
In applied mathematics, the reproducing kernel particle method is a meshfree computational method introduced in Liu et al.
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Smoothed finite element method
Smoothed finite element methods (S-FEM) are a particular class of numerical simulation algorithms for the simulation of physical phenomena.
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Smoothed-particle hydrodynamics
Smoothed-particle hydrodynamics (SPH) is a computational method used for simulating the mechanics of continuum media, such as solid mechanics and fluid flows.
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Stencil code
Stencil codes are a class of iterative kernels which update array elements according to some fixed pattern, called a stencil.
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Ted Belytschko
Ted Bohdan Belytschko (January 13, 1943 – September 15, 2014) was an American mechanical engineer.
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Types of mesh
In computational solutions of partial differential equations, meshing is a discrete representation of the geometry that is involved in the problem.
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Viscous vortex domains method
The viscous vortex domains (VVD) method is a mesh-free method of computational fluid dynamics for directly numerically solving 2D Navier-Stokes equations in Lagrange coordinates It doesn't implement any turbulence model and free of arbitrary parameters.
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Weak formulation
Weak formulations are important tools for the analysis of mathematical equations that permit the transfer of concepts of linear algebra to solve problems in other fields such as partial differential equations.
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Weakened weak form
Weakened weak form (or W2 form) is used in the formulation of general numerical methods based on meshfree methods and/or finite element method settings.
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Redirects here:
Meshfree method, Meshless method.
References
[1] https://en.wikipedia.org/wiki/Meshfree_methods
